This is what I threw on my scratchpad, plus two bug fixes:

sub maxima(&@)
{
    my $measure = shift @_;
    return   if  ! @_;
    my @maxima = shift @_;
    my $max;
    $max = $measure->( $_ )   for  @maxima;
    for( @_ ) {
        my $key = $measure->( $_ );
        if(  $max < $key  ) {
            @maxima = $_;
            $max = $key;
        } elsif(  $max == $key  ) {
            push @maxima, $_;
        }
    }
    return @maxima;
}

sub minima(&@)
{
    my $measure = shift @_;
    return   if  ! @_;
    my @minima = shift @_;
    my $min;
    $min = $measure->( $_ )   for  @minima;
    for( @_ ) {
        my $key = $measure->( $_ );
        if(  $key < $min  ) {
            $min = $key;
            @minima = $_;
        } elsif(  $key == $min  ) {
            push @minima, $_;
        }
    }
    return @minima;
}

sub strmaxima(&@)
{
    my $measure = shift @_;
    return   if  ! @_;
    my @maxima = shift @_;
    my $max;
    $max = $measure->( $_ )   for  @maxima;
    for( @_ ) {
        my $key = $measure->( $_ );
        if(  $max lt $key  ) {
            @maxima = $_;
            $max = $key;
        } elsif(  $max eq $key  ) {
            push @maxima, $_;
        }
    }
    return @maxima;
}

sub strminima(&@)
{
    my $measure = shift @_;
    return   if  ! @_;
    my @minima = shift @_;
    my $min;
    $min = $measure->( $_ )   for  @minima;
    for( @_ ) {
        my $key = $measure->( $_ );
        if(  $key lt $min  ) {
            @minima = $_;
            $min = $key;
        } elsif(  $key eq $min  ) {
            push @minima, $_;
        }
    }
    return @minima;
}
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Which I think would be fine additions to List::Util.

However, (Update: I added return   if  ! @_; to each because ) these should return an empty list not (undef) when given an empty list.